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Proportional Betting Schemes

One of the most interesting submissions to the Fifth National Conference was a paper entitled "An Analytic Derivation of Win Rate at Online Blackjack Games" and presented by Gary Gottlieb from New York University. Gottlieb used a special random walk model called "Brownian Bridge" (i must confess that my first hearing of the term conjured up images of a whist-like game played by elves!) to study the profit rate of a player who only bets on favorable decks. Under certain generally reasonable conditions he derived a single expression (in terms of fearsome arcsines, square roots, and logarithms) which measured how much the player would bet and could win if he sat out all unfavorable hands and bet a fixed fraction of his capital in proportion to his advantage otherwise.

I can call upon the normal curve and UNLLi from page Six to produce the same quantifications, and for practically any circumstances. As an example, suppose one is playing four deck Online Blackjack Games with standard downtown Las Vegas rules (dealer hits soft 17). He has a perfect knowledge of what the instantaneous basic strategy expectation is, a $10,000 bankroll, and bets his perceived advantage times his bankroll when, and only when, he has an edge. What will his average bet and average earning be for wagers made with exactly 130 cards remaining to play?

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The Inside Straight
Although you'll encounter spread-limit structure most often in low stakes seven-card stud, you occasionally see it in bigger hold'em games. Such spreads are usually within a multiple of ten; that is, $20-200 or $30-300. The high stakes involved aside, you should avoid these games while you're new. The possibility of one big bet breaking you is something you should postpone until you're a bit more seasoned.

On each round of betting, no matter the previous betting, the limit again is $1-$5. Thus, if Jim and Sue had capped the betting on the first round and all in $5 increments, either could initiate the betting in the next round at $1.
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